WASHINGTON — A record-setting crush of last-minute shoppers descended on HealthCare.gov on Monday, creating long wait times for users and putting new stress on the government’s much-maligned health portal as they raced against a midnight deadline to sign up for coverage that will go into effect Jan. 1.

More than 1 million people had logged on to the site by 5 p.m., officials said, five times more than the previous Monday. The flood of visitors quickly triggered a backup queuing system that invites users to come back during less-busy times. More than 60,000 people provided an email address Monday to get invitations to return, officials said.

The high volume of visitors also prompted White House officials to abruptly establish a 24-hour grace period that will effectively extend the deadline, allowing those who sign up Tuesday to still receive coverage starting Jan. 1.

Officials compared the last-minute decision to the kind often made by election officials to keep a polling place open late into the night to accommodate voters already in line at closing.

The grace period was the latest example of the administration’s willingness to fiddle with deadlines that once seemed set in political concrete. The botched rollout of the website has forced the White House to adjust its plans repeatedly in an attempt to accommodate users and avoid further examples of signs that the program is not ready for prime time.

“We have taken steps to make sure that those who tried to enroll today, but had delays due to high traffic, have a fail-safe,” said Julie Bataille, a spokeswoman for the federal Centers for Medicare & Medicaid Services.

Administration officials said there would be no more extensions. After Tuesday, people who sign up for insurance through HealthCare.gov should not expect to have coverage at the beginning of 2014, they said.

President Barack Obama’s aides are bracing for Republicans to seize on stories of people whose insurance was canceled because of the Affordable Care Act and who were unable to find a replacement by Jan. 1. Some of those people may appear at a hospital, a doctor’s office or a pharmacy and be told that they no longer have coverage.

“While the holiday surprises have become commonplace, the latest extension is another disappointment for the ‘most transparent administration in history,’” said Rep. Fred Upton, R-Mich., chairman of the House Energy and Commerce Committee.

Obama, vacationing in Hawaii with his family, offered a symbolic gesture to people who are using the government’s health care site to get insurance: White House officials announced Monday that the president had enrolled in a health insurance plan over the weekend using the District of Columbia’s website.

The president and his family receive health care through the military. But administration officials said they hoped that Obama’s gesture would set an example for many of the uninsured they were urging to sign up before the deadline.

The president opted for a bronze plan, one of the less-expensive options.

For many ordinary visitors who had postponed visiting the health care website, Monday was a frustrating day. While it appeared that the site did not crash or go offline, people calling the federal exchange Monday morning were greeted with a recorded message: “Welcome to the health insurance marketplace. We are currently experiencing longer-than-normal hold time. Do you need coverage for Jan. 1? Please stay on the line, as your call is important to us.”

Robert Zirkelbach, a spokesman for America’s Health Insurance Plans, a trade group, said insurers would “do everything they can to help consumers through the enrollment process and mitigate potential confusion or disruption caused by all of these last-minute changes to the rules and deadlines.”

He said insurers voluntarily extended a separate payment deadline last week. Consumers must pay the first month’s premium before coverage takes effect, he said, but those who pay by Jan. 10 will be able to have coverage retroactive to Jan. 1.

Michael D. Shear

and Robert Pear,

The New York Times

IN THE KNOW: Help from Parkland

Certified application counselors from the Parkland Health & Hospital system will be available Tuesday to assist patients with the health insurance enrollment process.

“We’re going to keep it going until 5 o’clock,” said Marian Morrow, patient financial services manager. She said she didn’t know how many people would show up on Christmas Eve, but “we just want to be prepared if they do come.”

Individuals can talk to a Parkland certified application counselor at the business office, 5201 Harry Hines Blvd. in Dallas, or at any of Parkland’s Community Oriented Primary Care health centers. They can also call 214-590-0333.

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